Solved papers for JEE Main & Advanced JEE Main Paper (Held on 08-4-2019 Afternoon)

done JEE Main Paper (Held on 08-4-2019 Afternoon) Total Questions - 90

• question_answer1) A circuit connected to an ac source of emf $e={{e}_{0}}\sin (100t)$with t in seconds, gives a phase difference of$\frac{\pi }{4}$ between the emf e and current i. Which of the following circuits will exhibit this?             [JEE Main 8-4-2019 Afternoon]

A)
RC circuit with $R=1k\Omega$and $C=1\mu F$

B)
RL circuit with $R=1k\Omega$ and L = 1mH

C)
RL circuit with $R=1k\Omega$ and L = 10 Mh

D)
RC circuit with $R=1k\Omega$ and $C=10\mu F$

• question_answer2) Two very long, straight, and insulated wires are kept at $90{}^\circ$ angle from each other in xy-plane as shown in the figure. These wires carry currents of equal magnitude I, whose directions are shown in the figure. The net magnetic field at point P will be :                     [JEE Main 8-4-2019 Afternoon] A)
Zero

B)
$\frac{+{{\mu }_{0}}I}{\pi d}(\hat{z})$

C)
$-\frac{{{\mu }_{0}}I}{2\pi d}(\hat{x}+\hat{y})$

D)
$\frac{{{\mu }_{0}}I}{2\pi d}(\hat{x}+\hat{y})$

• question_answer3) A common emitter amplifier circuit, built using an npn transistor, is shown in the figure. Its dc current gain is $250,{{R}_{C}}=1k\Omega$and ${{V}_{CC}}=10V.$ What is the minimum base current for ${{V}_{CE}}$ to reach saturation?  [JEE Main 8-4-2019 Afternoon] A)
$100\mu A$

B)
$7\mu A$

C)
$40\mu A$

D)
$10\mu A$

• question_answer4) A particle starts from origin O from rest and moves with a uniform acceleration along the positive x-axis. Identify all figures that correctly represent the motion qualitatively. (a = acceleration, v = velocity, x = displacement, t = time) [JEE Main 8-4-2019 Afternoon]  [A] [B] [C] [D] A)
[A], [B], [C]

B)
[A]

C)
[A], [B], [D]

D)
[B], [C]

• question_answer5) In the circuit shown, a four-wire potentiometer is made of a 400 cm long wire, which extends between A and B. The resistance per unit length of the potentiometer wire is $r=0.01\Omega /cm.$. If an ideal voltmeter is connected as shown with jockey J at 50 cm from end A, the expected reading of the voltmeter will be :-             [JEE Main 8-4-2019 Afternoon] A)
0.20 V

B)
0.25 V

C)
0.75 V

D)
0.50V

• question_answer6) A cell of internal resistance r drives current through an external resistance R. The power delivered by the cell to the external resistance will be maximum when :-             [JEE Main 8-4-2019 Afternoon]

A)
R = 1000 r

B)
R = 0.001 r

C)
R = 2r

D)
R = r

• question_answer7) An electric dipole is formed by two equal and opposite charges q with separation d. The charges have same mass m. It is kept in a uniform electric field E. If it is slightly rotated from its equilibrium orientation, then its angular frequency $\omega$is :- [JEE Main 8-4-2019 Afternoon]

A)
$\sqrt{\frac{qE}{2md}}$

B)
$\sqrt{\frac{qE}{md}}$

C)
$\sqrt{\frac{2qE}{md}}$

D)
$\sqrt{\frac{qE}{md}}$

• question_answer8) In a line of sight radio communication, a distance of about 50 km is kept between the transmitting and receiving antennas. If the height of the receiving antenna is 70m, then the minimum height of the transmitting antenna should be: (Radius of the Earth $=6.4\times {{10}^{6}}m$).                                                 [JEE Main 8-4-2019 Afternoon]

A)
40 m

B)
51 m

C)
32 m

D)
20 m

• question_answer9) The ratio of mass densities of nuclei of $^{40}Ca$and $^{16}O$is close to :-             [JEE Main 8-4-2019 Afternoon]

A)
1

B)
2

C)
0.1

D)
5

• question_answer10) Calculate the limit of resolution of a telescope objective having a diameter of 200 cm, if it has to detect light of wavelength 500 nm coming from a star :- [JEE Main 8-4-2019 Afternoon]

A)
$305\text{ }\times \text{ }10-9\text{ }radian$

B)
$152.5\text{ }\times \text{ }10-9\text{ }radian$

C)
$610\text{ }\times \text{ }10-9\text{ }radian$

D)
$457.5\text{ }\times \text{ }10-9\text{ }radian$

• question_answer11) The magnetic field of an electromagnetic wave is given by :- $\vec{B}=1.6\times {{10}^{-6}}\cos \left( 2\times {{10}^{7}}z+6\times {{10}^{15}}t \right)\left( 2\hat{i}+\hat{j} \right)\frac{Wb}{{{m}^{2}}}$The associated electric field will be :-                                                                                     [JEE Main 8-4-2019 Afternoon]

A)
$\vec{E}=4.8\times {{10}^{2}}\cos \left( 2\times {{10}^{7}}z+6\times {{10}^{15}}t \right)\left( \hat{i}-2\hat{j} \right)\frac{V}{m}$

B)
$\vec{E}=4.8\times {{10}^{2}}\cos \left( 2\times {{10}^{7}}z-6\times {{10}^{15}}t \right)\left( 2\hat{i}+\hat{j} \right)\frac{V}{m}$

C)
$\vec{E}=4.8\times {{10}^{2}}\cos \left( 2\times {{10}^{7}}z-6\times {{10}^{15}}t \right)\left( -2\hat{j}+\hat{i} \right)\frac{V}{m}$

D)
$\vec{E}=4.8\times {{10}^{2}}\cos \left( 2\times {{10}^{7}}z+6\times {{10}^{15}}t \right)\left( -\hat{i}+2\hat{j} \right)\frac{V}{m}$

• question_answer12) Young's moduli of two wires A and B are in the ratio 7 : 4. Wire A is 2 m long and has radius R. Wire B is 1.5 m long and has radius 2 mm. If the two wires stretch by the same length for a given load, then the value of R is close to :-                                                                  [JEE Main 8-4-2019 Afternoon]

A)
1.9 mm

B)
1.7 mm

C)
1.5 mm

D)
1.3 mm

• question_answer13) A rocket has to be launched from earth in such a way that it never returns. If E is the minimum energy delivered by the rocket launcher, what should be the minimum energy that the launcher should have if the same rocket is to be launched from the surface of the moon? Assume that the density of the earth and the moon are equal and that the earth's volume is 64 times the volume of the moon :-               [JEE Main 8-4-2019 Afternoon]

A)
$\frac{E}{4}$

B)
$\frac{E}{16}$

C)
$\frac{E}{32}$

D)
$\frac{E}{64}$

• question_answer14) A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights ${{h}_{sph}}$and ${{h}_{cyl}}$on the incline. The ratio $\frac{{{h}_{sph}}}{{{h}_{cyl}}}$is given by :-   [JEE Main 8-4-2019 Afternoon] A)
$\frac{14}{15}$

B)
$\frac{4}{5}$

C)
1

D)
$\frac{2}{\sqrt{5}}$

• question_answer15) The given diagram shows four processes i.e., isochoric, isobaric, isothermal and adiabatic. The correct assignment of the processes, in the same order is given by:-                      [JEE Main 8-4-2019 Afternoon] A)
d a c b

B)
a d c b

C)
a d b c

D)
d a b c

• question_answer16) A positive point charge is released from rest at a distance${{r}_{0}}$from a positive line charge with uniform density. The speed (v) of the point charge, as a function of instantaneous distance r from line charge, is proportional to :-                                          [JEE Main 8-4-2019 Afternoon] A)
$\text{v}\propto {{\text{e}}^{+r/{{r}_{0}}}}$

B)
$\text{v}\propto \ell n\left( \frac{r}{{{r}_{0}}} \right)$

C)
$\text{v}\propto \left( \frac{r}{{{r}_{0}}} \right)$

D)
$\text{v}\propto \sqrt{\ell n\left( \frac{r}{{{r}_{0}}} \right)}$

• question_answer17) A damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half its value for every 10 oscillations. The time it will take to drop to $\frac{1}{1000}$of the original amplitude is close to :- [JEE Main 8-4-2019 Afternoon]

A)
100 s

B)
20 s

C)
10 s

D)
50 s

• question_answer18) The electric field in a region is given by $\overrightarrow{E}=\left( Ax+B \right)\hat{i},$ where E is in $N{{C}^{-1}}$ and x is in metres. The values of constants are A = 20 SI unit and B = 10 SI unit. If the potential at x = 1 is ${{V}_{1}}$and that at x = -5 is ${{V}_{2}}$, then ${{V}_{1}}-{{V}_{2}}$ is :-                                                                                                             [JEE Main 8-4-2019 Afternoon]

A)
- 48 V

B)
- 520 V

C)
180 V

D)
320 V

• question_answer19) A parallel plate capacitor has$1\mu F$ capacitance. One of its two plates is given$+2\mu C$charge and the other plate, $+4\mu C$ charge. The potential difference developed across the capacitor is:- [JEE Main 8-4-2019 Afternoon]

A)
5V

B)
2V

C)
3V

D)
1V

• question_answer20) In a simple pendulum experiment for determination of acceleration due to gravity (g), time taken for 20 oscillations is measured by using a watch of 1 second least count. The mean value of time taken comes out to be 30 s. The length of pendulum is measured by using a meter scale of least count 1 mm and the value obtained is 55.0 cm. The percentage error in the determination of g is close to:- [JEE Main 8-4-2019 Afternoon]

A)
0.7%

B)
0.2%

C)
3.5%

D)
6.8%

• question_answer21) A uniform rectangular thin sheet ABCD of mass M has length a and breadth b, as shown in the figure. If the shaded portion HBGO is cut-off, the coordinates of the centre of mass of the remaining portion will be :- [JEE Main 8-4-2019 Afternoon] A)
$\left( \frac{2a}{3},\frac{2b}{3} \right)$

B)
$\left( \frac{5a}{3},\frac{5b}{3} \right)$

C)
$\left( \frac{3a}{4},\frac{3b}{4} \right)$

D)
$\left( \frac{5a}{12},\frac{5b}{12} \right)$

• question_answer22) The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth, is closest to:  [Boltzmann Constant ${{k}_{B}}=1.38\times {{10}^{-23}}J/K$ Avogadro Number ${{N}_{A}}=6.02\times {{10}^{26}}/kg$ Radius of Earth : $6.4\times {{10}^{6}}m$ Gravitational acceleration on Earth$=10m{{s}^{-2}}$]
[JEE Main 8-4-2019 Afternoon]

A)
650 K

B)
$3\times {{10}^{5}}K$

C)
${{10}^{4}}$ K

D)
800 K

• question_answer23) A convex lens (of focal length 20 cm) and a concave mirror, having their principal axes along the same lines, are kept 80 cm apart from each other. The concave mirror is to the right of the convex lens. When an object is kept at a distance of 30 cm to the left of the convex lens, its image remains at the same position even if the concave mirror is removed. The maximum distance of the object for which this concave mirror, by itself would produce a virtual image would be :- [JEE Main 8-4-2019 Afternoon]

A)
20 cm

B)
10 cm

C)
25 cm

D)
30 cm

• question_answer24) A rectangular solid box of length 0.3 m is held horizontally, with one of its sides on the edge of a platform of height 5m. When released, it slips off the table in a very short time $\tau =0.01s,$ remaining essentially horizontal. The angle by which it would rotate when it hits the ground will be (in radians) close to :- [JEE Main 8-4-2019 Afternoon] A)
0.02

B)
0.28

C)
0.5

D)
0.3

• question_answer25) If surface tension (S), Moment of inertia (I) and Planck's constant (h), were to be taken as the fundamental units, the dimensional formula for linear momentum would be :- [JEE Main 8-4-2019 Afternoon]

A)
${{S}^{3/2}}{{I}^{1/2}}{{h}^{0}}$

B)
${{S}^{1/2}}{{I}^{1/2}}{{h}^{0}}$

C)
${{S}^{1/2}}{{I}^{1/2}}{{h}^{-1}}$

D)
${{S}^{1/2}}{{I}^{3/2}}{{h}^{-1}}$

• question_answer26) In the figure shown, what is the current (in Ampere) drawn from the battery? You are given: ${{R}_{1}}=15\Omega ,{{R}_{2}}=10\Omega ,{{R}_{3}}=20\Omega ,{{R}_{4}}=5\Omega ,$ ${{R}_{5}}=25\Omega ,{{R}_{6}}=30\Omega ,E=15V$             [JEE Main 8-4-2019 Afternoon] A)
7/18

B)
13/24

C)
9/32

D)
20/3

• question_answer27) A nucleus A, with a finite de-Broglie wavelength ${{\lambda }_{A}},$undergoes spontaneous fission into two nuclei B and C of equal mass. B flies in the same direction as that of A, while C flies in the opposite direction with a velocity equal to half of that of B. The de-Broglie wavelengths ${{\lambda }_{B}}$and ${{\lambda }_{C}}$ of B and C are respectively :- [JEE Main 8-4-2019 Afternoon]

A)
$2{{\lambda }_{A}},{{\lambda }_{A}}$

B)
${{\lambda }_{A}},2{{\lambda }_{A}}$

C)
${{\lambda }_{A}},\frac{{{\lambda }_{A}}}{2}$

D)
$\frac{{{\lambda }_{A}}}{2},{{\lambda }_{A}}$

• question_answer28)           A body of mass ${{m}_{1}}$ moving with an unknown velocity of ${{\text{v}}_{1}}\hat{i},$undergoes a collinear collision with a body of mass${{m}_{2}}$moving with a velocity ${{\text{v}}_{2}}\hat{i}.$After collision, ${{m}_{1}}$and ${{m}_{2}}$move with velocities of ${{\text{v}}_{3}}\hat{i}$and ${{\text{v}}_{4}}\hat{i},$respectively. If ${{m}_{2}}=0.5{{m}_{1}}$and ${{\text{v}}_{3}}=0.5{{\text{v}}_{1}},$then ${{\text{v}}_{1}}$is :-                                                             [JEE Main 8-4-2019 Afternoon]

A)
${{\text{v}}_{4}}-\frac{{{\text{v}}_{2}}}{4}$

B)
${{\text{v}}_{4}}-\frac{{{\text{v}}_{2}}}{2}$

C)
${{\text{v}}_{4}}-{{\text{v}}_{2}}$

D)
${{\text{v}}_{4}}\text{+}{{\text{v}}_{2}}$

• question_answer29) Let$\left| {{{\vec{A}}}_{1}} \right|=3,\left| {{{\vec{A}}}_{2}} \right|=5$and$\left| {{{\vec{A}}}_{1}}+{{{\vec{A}}}_{2}} \right|=5.$The value of$\left( 2{{{\vec{A}}}_{1}}+3{{{\vec{A}}}_{2}} \right).\left( 3{{{\vec{A}}}_{1}}-2{{{\vec{A}}}_{2}} \right)$is :- [JEE Main 8-4-2019 Afternoon]

A)
-112.5

B)
-106.5

C)
-118.5

D)
-99.5

• question_answer30) Two magnetic dipoles X and Y are placed at a separation d, with their axes perpendicular to each other. The dipole moment of Y is twice that of X. A particle of charge q is passing, through their midpoint P, at angle $\theta ={{45}^{o}}$with the horizontal line, as shown in figure. What would be the magnitude of force on the particle at that instant? (d is much larger than the dimensions of the dipole)             [JEE Main 8-4-2019 Afternoon] A)
$\sqrt{2}\left( \frac{{{\mu }_{0}}}{4\pi } \right)\frac{M}{{{(d/2)}^{3}}}\times q\text{v}$

B)
$\left( \frac{{{\mu }_{0}}}{4\pi } \right)\frac{2M}{{{(d/2)}^{3}}}\times q\text{v}$

C)
$\left( \frac{{{\mu }_{0}}}{4\pi } \right)\frac{M}{{{(d/2)}^{3}}}\times q\text{v}$

D)
0

• question_answer31) Calculate the standard cell potential in(V) of the cell in which following reaction takes place:  $F{{e}^{2+}}(aq)+A{{g}^{+}}(aq)\to F{{e}^{3+}}(aq)+Ag(s)$ Given that $E_{A{{g}^{+}}/Ag}^{o}=xV$ $E_{F{{e}^{2+}}/Fe}^{o}=yV$ $E_{F{{e}^{3+}}/Fe}^{o}=zV$
[JEE Main 8-4-2019 Afternoon]

A)
$x+2y-3z$

B)
$x-z$

C)
$x-y$

D)
$x+y-z$

• question_answer32) The major product in the following reaction is : [JEE Main 8-4-2019 Afternoon]

A) B) C) D) • question_answer33) For the following reactions, equilibrium constants are given : $S(s)+{{O}_{2}}(g)\rightleftharpoons S{{O}_{2}}(g);{{K}_{1}}={{10}^{52}}$ $2S(s)+3{{O}_{2}}(g)\rightleftharpoons 2S{{O}_{3}}(g);{{K}_{2}}={{10}^{129}}$ The equilibrium constant for the reaction, $2S{{O}_{2}}(g)+{{O}_{2}}(g)\rightleftharpoons 2S{{O}_{3}}(g)$is             [JEE Main 8-4-2019 Afternoon]

A)
${{10}^{181}}$

B)
${{10}^{154}}$

C)
${{10}^{25}}$

D)
${{10}^{77}}$

• question_answer34) The ion that has $s{{p}^{3}}{{d}^{2}}$hybridization for the central atom, is : [JEE Main 8-4-2019 Afternoon]

A)
${{[IC{{I}_{2}}]}^{-}}$

B)
${{[I{{F}_{6}}]}^{-}}$

C)
${{[IC{{I}_{4}}]}^{-}}$

D)
${{[Br{{F}_{2}}]}^{-}}$

• question_answer35) The structure of Nylon-6 is : [JEE Main 8-4-2019 Afternoon]

A) B) C) D) • question_answer36) The major product of the following reaction is: [JEE Main 8-4-2019 Afternoon]

A) B) C) D) • question_answer37) The major product of the following reaction is: [JEE Main 8-4-2019 Afternoon]

A) B) C) D) • question_answer38) The percentage composition of carbon by mole in methane is : [JEE Main 8-4-2019 Afternoon]

A)
80%

B)
25%

C)
75%

D)
20%

• question_answer39) The IUPAC symbol for the element with atomic number 119 would be : [JEE Main 8-4-2019 Afternoon]

A)
unh

B)
uun

C)
une

D)
uue

• question_answer40) The compound that inhibits the growth of tumors is : [JEE Main 8-4-2019 Afternoon]

A)
$cis-[Pd{{(Cl)}_{2}}{{(N{{H}_{3}})}_{2}}]$

B)
$cis-[Pt{{(Cl)}_{2}}{{(N{{H}_{3}})}_{2}}]$

C)
$trans-[Pt{{(Cl)}_{2}}{{(N{{H}_{3}})}_{2}}]$

D)
$trans-[Pd{{(Cl)}_{2}}{{(N{{H}_{3}})}_{2}}]$

• question_answer41) The covalent alkaline earth metal halide (X = Cl, Br, I) is : [JEE Main 8-4-2019 Afternoon]

A)
$Ca{{X}_{2}}$

B)
$Sr{{X}_{2}}$

C)
$Be{{X}_{2}}$

D)
$Mg{{X}_{2}}$

• question_answer42) The major product obtained in the following reaction is : [JEE Main 8-4-2019 Afternoon]

A) B) C) D) • question_answer43) The statement that is INCORRECT about the interstitial compounds is : [JEE Main 8-4-2019 Afternoon]

A)
They have high melting points

B)
They are chemically reactive

C)
They have metallic conductivity

D)
They are very hard

• question_answer44) The maximum prescribed concentration of copper in drinking water is: [JEE Main 8-4-2019 Afternoon]

A)
5 ppm

B)
0.5 ppm

C)
0.05 ppm

D)
3 ppm

• question_answer45) The calculated spin-only magnetic moments (BM) of the anionic and cationic species of ${{[Fe{{({{H}_{2}}O)}_{6}}]}_{2}}$and $[Fe{{(CN)}_{6}}],$respectively, are : [JEE Main 8-4-2019 Afternoon]

A)
4.9 and 0

B)
2.84 and 5.92

C)
0 and 4.9

D)
0 and 5.92

• question_answer46) 0.27 g of a long chain fatty acid was dissolved in $100c{{m}^{3}}$of hexane. 10 mL of this solution was added drop wise to the surface of water in a round watch glass. Hexane evaporates and a monolayer is formed. The distance from edge to centre of the watch glass is 10 cm. What is the height of the monolayer? [Density of fatty acid $=0.9g\,c{{m}^{-3}},\pi =3$]             [JEE Main 8-4-2019 Afternoon]

A)
${{10}^{-8}}m$

B)
${{10}^{-6}}m$

C)
${{10}^{-4}}m$

D)
${{10}^{-2}}m$

• question_answer47) Among the following molecules / ions, $C_{2}^{2-},N_{2}^{2-},O_{2}^{2-},{{O}_{2}}$ which one is diamagnetic and has the shortest bond length?             [JEE Main 8-4-2019 Afternoon]

A)
$C_{2}^{2-}$

B)
$N_{2}^{2-}$

C)
$O_{2}^{{}}$

D)
$O_{2}^{2-}$

• question_answer48) 5 moles of an ideal gas at 100 K are allowed to undergo reversible compression till its temperature becomes 200 K. If ${{C}_{V}}=28\,J{{K}^{-1}}mo{{l}^{-1}},$calculate $\Delta U$and $\Delta pV$ for this process. $(R=8.0J{{K}^{-1}}mo{{l}^{-1}})$             [JEE Main 8-4-2019 Afternoon]

A)
$\Delta U=14\,kJ;\,\,\,\,\,\Delta (pV)=4\,kJ$

B)
$\Delta U=14\,kJ;\,\,\,\,\,\Delta (pV)=18\,kJ$

C)
$\Delta U=2.8\,kJ;\,\,\,\,\,\Delta (pV)=0.8\,kJ$

D)
$\Delta U=14\,kJ;\,\,\,\,\,\Delta (pV)=0.8\,kJ$

• question_answer49) Which one of the following alkenes when treated with HCl yields majorly an anti Markovnikov product? [JEE Main 8-4-2019 Afternoon]

A)
${{F}_{3}}C-CH=C{{H}_{2}}$

B)
$Cl-CH=C{{H}_{2}}$

C)
$C{{H}_{3}}O-CH=C{{H}_{2}}$

D)
${{H}_{2}}N-CH=C{{H}_{2}}$

• question_answer50) For a reaction scheme $A\xrightarrow[{}]{{{k}_{1}}}B\xrightarrow[{}]{{{k}_{2}}}C,$ if the rate of formation of B is set to be zero then the concentration of B is given by: [JEE Main 8-4-2019 Afternoon]

A)
$\left( \frac{{{k}_{1}}}{{{k}_{2}}} \right)[A]$

B)
$({{k}_{1}}+{{k}_{2}})[A]$

C)
${{k}_{1}}{{k}_{2}}[A]$

D)
$({{k}_{1}}-{{k}_{2}})[A]$

• question_answer51) Which of the following compounds will show the maximum enol content? [JEE Main 8-4-2019 Afternoon]

A)
$C{{H}_{3}}COC{{H}_{2}}COC{{H}_{3}}$

B)
$C{{H}_{3}}COC{{H}_{3}}$

C)
$C{{H}_{3}}COC{{H}_{2}}CON{{H}_{2}}$

D)
$C{{H}_{3}}COC{{H}_{2}}COO{{C}_{2}}{{H}_{5}}$

• question_answer52) The correct statement about $IC{{l}_{5}}$and $ICl_{4}^{-}$ is [JEE Main 8-4-2019 Afternoon]

A)
$IC{{l}_{5}}$is trigonal bipyramidal and$ICl_{4}^{-}$is tetrahedral.

B)
$IC{{l}_{5}}$is square pyramidal and$ICl_{4}^{-}$is tetrahedral.

C)
$ICl_{5}^{{}}$is square pyramidal and $ICl_{4}^{-}$is square planar.

D)
Both are isostructural.

• question_answer53) The major product obtained in the following reaction is [JEE Main 8-4-2019 Afternoon]

A) B) C) D) • question_answer54) Fructose and glucose can be distinguished by: [JEE Main 8-4-2019 Afternoon]

A)
Fehling's test

B)
Barcode?s test

C)
Benedict's test

D)
Seliwanoff's test

• question_answer55) If p is the momentum of the fastest electron ejected from a metal surface after the irradiation of light having wavelength $\lambda$, then for 1.5 p momentum of the photoelectron, the wavelength of the light should be: (Assume kinetic energy of ejected photoelectron to be very high in comparison to work function)             [JEE Main 8-4-2019 Afternoon]

A)
$\frac{1}{2}\lambda$

B)
$\frac{3}{4}\lambda$

C)
$\frac{2}{3}\lambda$

D)
$\frac{4}{9}\lambda$

• question_answer56) Consider the bcc unit cells of the solids 1 and 2 with the position of atoms as shown below. The radius of atom B is twice that of atom A. The unit cell edge length is 50% more in solid 2 than in 1. What is the approximate packing efficiency in solid 2?             [JEE Main 8-4-2019 Afternoon] A)
45%

B)
65%

C)
90%

D)
75%

• question_answer57) Poly substitution is a major drawback in: [JEE Main 8-4-2019 Afternoon]

A)
Reimer Tiemann reaction

B)
Friedel Craft's acylation

C)
Friedel Craft's alkylation

D)
Acetylation of aniline

• question_answer58) The Mond process is used for the [JEE Main 8-4-2019 Afternoon]

A)
extraction of Mo

B)
Purification of Ni

C)
Purification of Zr and Ti

D)
Extraction of Zn

• question_answer59) The strength of 11.2 volume solution of ${{H}_{2}}{{O}_{2}}$ is : [Given that molar mass of $H=1g\,mo{{l}^{-1}}$and $O=16g\,mo{{l}^{-1}}$] [JEE Main 8-4-2019 Afternoon]

A)
13.6%

B)
3.4%

C)
34%

D)
1.7%

• question_answer60) For the solution of the gases w, x, y and z in water at 298K, the Henrys law constants $({{K}_{H}})$ are 0.5, 2, 35 and 40 kbar, respectively. The correct plot for the given data is :- [JEE Main 8-4-2019 Afternoon]

A) B) C) D) • question_answer61) The minimum number of times one has to  toss a fair coin so that the probability of observing at least one head is at least 90% is: [JEE Main 8-4-2019 Afternoon]

A)
5

B)
3

C)
2

D)
4

• question_answer62) A student scores the following marks in five tests : 45,54,41,57,43. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is                         [JEE Main 8-4-2019 Afternoon]

A)
$\frac{10}{\sqrt{3}}$

B)
$\frac{100}{\sqrt{3}}$

C)
$\frac{100}{3}$

D)
$\frac{10}{3}$

• question_answer63) The sum$\sum\limits_{k=1}^{20}{k\frac{1}{{{2}^{k}}}}$is equal to- [JEE Main 8-4-2019 Afternoon]

A)
$2-\frac{3}{{{2}^{17}}}$

B)
$2-\frac{11}{{{2}^{19}}}$

C)
$1-\frac{11}{{{2}^{20}}}$

D)
$2-\frac{21}{{{2}^{20}}}$

• question_answer64) Let $\vec{a}=3\hat{i}+2\hat{j}+x\hat{k}$and$\vec{b}=\hat{i}-\hat{j}+\hat{k},$for some real x. Then $\left| \vec{a}\times \vec{b} \right|=r$is possible if : [JEE Main 8-4-2019 Afternoon]

A)
$3\sqrt{\frac{3}{2}}<r<5\sqrt{\frac{3}{2}}$

B)
$0<r\le \sqrt{\frac{3}{2}}$

C)
$\sqrt{\frac{3}{2}}<r\le 3\sqrt{\frac{3}{2}}$

D)
$r\ge 5\sqrt{\frac{3}{2}}$

• question_answer65) If the system of linear equations  $x2y+kz=1$ $2x+y+z=2$ $3xykz=3$ has a solution $(x,y,z),z\ne 0,$then (x,y) lies on the straight line whose equation is :
[JEE Main 8-4-2019 Afternoon]

A)
$3x4y1=0$

B)
$3x4y4=0$

C)
$4x3y4=0$

D)
$4x3y1=0$

• question_answer66) If the eccentricity of the standard hyperbola passing through the point (4,6) is 2, then the equation of the tangent to the hyperbola at (4,6) is- [JEE Main 8-4-2019 Afternoon]

A)
$2xy2=0$

B)
$3x2y=0$

C)
$2x3y+10=0$

D)
$x2y+8=0$

• question_answer67) If the lengths of the sides of a triangle are in A.P. and the greatest angle is double the smallest, then a ratio of lengths of the sides of this triangle is :                                                  [JEE Main 8-4-2019 Afternoon]

A)
5 : 9 : 13

B)
5 : 6 : 7

C)
4 : 5 : 6

D)
3 : 4 : 5

• question_answer68) Let $f(x)={{a}^{x}}(a>0)$ be written as $f(x)={{f}_{1}}(x)+{{f}_{2}}(x,)$ where ${{f}_{1}}(x)$ is an even function of ${{f}_{2}}(x)$ is an odd function. Then ${{f}_{1}}(x+y)+{{f}_{1}}(x-y)$equals [JEE Main 8-4-2019 Afternoon]

A)
$2{{f}_{1}}(x){{f}_{1}}(y)$

B)
$2{{f}_{1}}(x){{f}_{2}}(y)$

C)
$2{{f}_{1}}(x+y){{f}_{2}}(x-y)$

D)
$2{{f}_{1}}(x+y){{f}_{1}}(x-y)$

• question_answer69) If the fourth term in the binomial expansion of${{\left( \sqrt{\frac{1}{{{x}^{1+{{\log }_{10}}x}}}}+{{x}^{\frac{1}{12}}} \right)}^{6}}$is equal to 200, and$x>1,$ then the value of x is : [JEE Main 8-4-2019 Afternoon]

A)
${{10}^{3}}$

B)
100

C)
${{10}^{4}}$

D)
10

• question_answer70) Let$S(\alpha )=\{(x,y):{{y}^{2}}\le x,0\le x\le \alpha \}$ and $A(\alpha )$is area of the region $S(\alpha )$. If for a $\lambda ,0<\lambda <4,A(\lambda ):A(4)=2:5,$then $\lambda$ equals [JEE Main 8-4-2019 Afternoon]

A)
$2{{\left( \frac{4}{25} \right)}^{\frac{1}{3}}}$

B)
$4{{\left( \frac{4}{25} \right)}^{\frac{1}{3}}}$

C)
$2{{\left( \frac{2}{5} \right)}^{\frac{1}{3}}}$

D)
$4{{\left( \frac{2}{5} \right)}^{\frac{1}{3}}}$

• question_answer71) Given that the slope of the tangent to a curve $y=y(x)$ at any point (x,y) is $\frac{2y}{{{x}^{2}}}.$ If the curve passes through the centre of the circle  ${{x}^{2}}+{{y}^{2}}2x2y=0,$ then its equation is : [JEE Main 8-4-2019 Afternoon]

A)
$x{{\log }_{e}}|y|=2(x-1)$

B)
$x{{\log }_{e}}|y|=x-1$

C)
${{x}^{2}}{{\log }_{e}}|y|=-2(x-1)$

D)
$x{{\log }_{e}}|y|=-2(x-1)$

• question_answer72) The vector equation of the plane through the line of intersection of the planes $x+y+z=1$and $2x+3y+4z=5$which is perpendicular to the plane $xy+z=0$ is :             [JEE Main 8-4-2019 Afternoon]

A)
$\vec{r}\times (\hat{i}+\hat{k})+2=0$

B)
$\vec{r}.(\hat{i}-\hat{k})-2=0$

C)
$\vec{r}.(\hat{i}-\hat{k})+2=0$

D)
$\vec{r}\times (\hat{i}-\hat{k})+2=0$

• question_answer73) Which one of the following statements is not a tautology ?             [JEE Main 8-4-2019 Afternoon]

A)
$(p\wedge q)\to p$

B)
$(p\wedge q)\to (\tilde{\ }p)\vee q$

C)
$p\to (p\vee q)$

D)
$(p\vee q)\to (p\vee (\tilde{\ }q))$

• question_answer74) Let $f:R\to R$be a differentiable function satisfying$f'(3)+f'(2)=0$ Then$\underset{x\to 0}{\mathop{\lim }}\,{{\left( \frac{1+f(3+x)-f(3)}{1+f(2-x)-f(2)} \right)}^{\frac{1}{x}}}$is equal to                                      [JEE Main 8-4-2019 Afternoon]

A)
${{e}^{2}}$

B)
$e$

C)
${{e}^{-1}}$

D)
1

• question_answer75) The tangent to the parabola ${{y}^{2}}=4x$at the point where it intersects the circle ${{x}^{2}}+{{y}^{2}}=5$in the first quadrant, passes through the point: [JEE Main 8-4-2019 Afternoon]

A)
$\left( -\frac{1}{3},\frac{4}{3} \right)$

B)
$\left( -\frac{1}{4},\frac{1}{2} \right)$

C)
$\left( \frac{3}{4},\frac{7}{4} \right)$

D)
$\left( \frac{1}{4},\frac{3}{4} \right)$

• question_answer76) Let the number 2, b, c be in an A.P. and $A=\left[ \begin{matrix} 1 & 1 & 1 \\ 2 & b & c \\ 4 & {{b}^{2}} & {{c}^{2}} \\ \end{matrix} \right].$If det $(A)\in [2,16],$then c lies in the interval :    [JEE Main 8-4-2019 Afternoon]

A)
$[2,3)$

B)
$(2+{{2}^{3/4}},4)$

C)
$[3,2+{{2}^{3/4}}]$

D)
$[4,6]$

• question_answer77) If three distinct numbers a,b,c are in G.P. and the equations $a{{x}^{2}}+2bx+c=0$and $d{{x}^{2}}+2ex+f=0$have a common root, then which one of the following statements is correct?                                                                                                             [JEE Main 8-4-2019 Afternoon]

A)
d, e, ? are in A.P.

B)
$\frac{d}{a},\frac{e}{b},\frac{f}{c}$a b c are in G.P.

C)
$\frac{d}{a},\frac{e}{b},\frac{f}{c}$are in A.P.

D)
d, e, ? are in G.P.

• question_answer78) The number of integral values of m for which the equation $(1+{{m}^{2}}){{x}^{2}}-2(1+3m)x+(1+8m)=0$  has no real root is :                                                [JEE Main 8-4-2019 Afternoon]

A)
infinitely many

B)
2

C)
3

D)
1

• question_answer79) If a point R(4,y,z) lies on the line segment joining the points P(2,-3,4) and Q(8,0,10), then the distance of R from the origin is :                                                                                        [JEE Main 8-4-2019 Afternoon]

A)
$2\sqrt{14}$

B)
6

C)
$\sqrt{53}$

D)
$2\sqrt{21}$

• question_answer80) If $z=\frac{\sqrt{3}}{2}+\frac{i}{2}\left( i=\sqrt{-1} \right),$then ${{(1+iz+{{z}^{5}}+i{{z}^{8}})}^{9}}$is equal to [JEE Main 8-4-2019 Afternoon]

A)
-1

B)
1

C)
0

D)
${{(-1+2i)}^{9}}$

• question_answer81) Let$f(x)=\int\limits_{0}^{x}{g}(t)dt,$ where g is a non-zero even function. If $f(x+5)=g(x),$then $\int\limits_{0}^{x}{f}(t)dt$equals- [JEE Main 8-4-2019 Afternoon]

A)
$\int\limits_{x+5}^{5}{g}(t)dt$

B)
$5\int\limits_{x+5}^{5}{g}(t)dt$

C)
$\int\limits_{5}^{x+5}{g}(t)dt$

D)
$2\int\limits_{5}^{x+5}{g}(t)dt$

• question_answer82) The tangent and the normal lines at the point $\left( \sqrt{3},1 \right)$ to the circle ${{x}^{2}}+{{y}^{2}}=4$ and the x-axis form a triangle. The area of this triangle (in square units) is:             [JEE Main 8-4-2019 Afternoon]

A)
$\frac{1}{3}$

B)
$\frac{4}{\sqrt{3}}$

C)
$\frac{1}{\sqrt{3}}$

D)
$\frac{2}{\sqrt{3}}$

• question_answer83) In an ellipse, with centre at the origin, if the difference of the lengths of major axis and minor axis is 10 and one of the foci is at $\left( 0,5\sqrt{3} \right),$ then the length of its latus rectum is: [JEE Main 8-4-2019 Afternoon]

A)
10

B)
8

C)
5

D)
6

• question_answer84) If $\left( 1 \right)=1,'\left( 1 \right)=3,$ then the derivative of $\left( \left( \left( x \right) \right) \right)+\left( \left( x \right) \right)2$ at x = 1 is : [JEE Main 8-4-2019 Afternoon]

A)
12

B)
33

C)
9

D)
15

• question_answer85) If $\int_{{}}^{{}}{\frac{dx}{{{x}^{3}}{{(1+{{x}^{6}})}^{2/3}}}}=xf(x){{\left( 1+{{x}^{6}} \right)}^{\frac{1}{3}}}+C$ where C is a constant of integration, then the function ?(x) is equal to-             [JEE Main 8-4-2019 Afternoon]

A)
$-\frac{1}{6{{x}^{3}}}$

B)
$\frac{3}{{{x}^{2}}}$

C)
$-\frac{1}{2{{x}^{2}}}$

D)
$-\frac{1}{2{{x}^{3}}}$

• question_answer86) Suppose that the points (h, k), (1,2) and (-3,4) lie on the line ${{L}_{1}}$. If a line ${{L}_{2}}$ passing through the points (h, k) and (4,3) is perpendicular to ${{L}_{1}}$, then $\frac{k}{h}$equals : [JEE Main 8-4-2019 Afternoon]

A)
3

B)
$-\frac{1}{7}$

C)
$\frac{1}{3}$

D)
0

• question_answer87) Let $f:[-1,3]\to R$be defined as  $f(x)=\left\{ \begin{matrix} \left| x \right|+\left[ x \right] & , & -l\le x [JEE Main 8-4-2019 Afternoon] A) four or more points B) only one point C) only two points D) only three points View Answer play_arrow • question_answer88) Two vertical poles of heights, 20m and 80m stand a part on a horizontal plane. The height (in meters) of the point of intersection of the lines joining the top of each pole to the foot of the other, from this horizontal plane is : [JEE Main 8-4-2019 Afternoon] A) 12 B) 15 C) 16 D) 18 View Answer play_arrow • question_answer89) The number of four-digit numbers strictly greater than 4321 that can be formed using the digits 0,1,2,3,4,5 (repetition of digits is allowed) is : [JEE Main 8-4-2019 Afternoon] A) 288 B) 306 C) 360 D) 310 View Answer play_arrow • question_answer90) The height of a right circular cylinder of maximum volume inscribed in a sphere of radius 3 is [JEE Main 8-4-2019 Afternoon] A) \[2\sqrt{3}$

B)
$\sqrt{3}$

C)
$\sqrt{6}$

D)
$\frac{2}{3}\sqrt{3}$

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